Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up through 2018 Q1. The test period is a forecast for 2018 Q2 and includes comparison to the observed median rent estimates for data collected in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-07-31




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 298.1040 224.3081 224.6182 209.2248 209.3826
Training 327.7931 181.3767 182.3301 184.4603 183.5038



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 245.0776 157.7657 157.9448 145.9491 146.0930
Training 252.5734 131.7601 132.2252 135.0159 134.3125



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -207.7519 -610.7231 -609.5783 -612.2685 -613.3433



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -207.2292 -594.3007 -593.205 -595.4383 -595.6145

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 63.9847 4.4864 55.5442 63.8542 73.2052 63.6303
Precision for idtract 38.9281 5.8628 28.6124 38.5158 51.6464 37.7281
Precision for idqtr 15949.5520 14657.0261 2529.0427 11729.9267 56269.8122 6479.4560
Rho for idqtr 0.0375 0.5657 -0.9084 0.0498 0.9325 0.8304
Precision for idqtr1 16973.3834 15165.6127 2744.5908 12655.1901 58671.6432 7031.8542



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 63.4486 4.4736 55.0310 63.3190 72.6420 63.0984
Precision for idtract (iid component) 91.7584 22.4883 55.1680 89.2126 143.1802 84.3796
Precision for idtract (spatial component) 138.3287 51.7935 65.9393 128.6129 266.2861 111.7279
Precision for idqtr 15123.1663 12024.6650 2954.7892 11819.4806 48574.4538 7356.6972
Rho for idqtr 0.0330 0.5723 -0.9121 0.0402 0.9388 0.8658
Precision for idqtr1 14786.2703 11768.5445 2858.5962 11555.7218 47627.9625 7162.2289



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 63.6801 4.5055 55.2173 63.5439 72.9529 63.3041
Precision for idtract (iid component) 91.0658 22.2517 55.2551 88.4090 142.1434 83.3448
Precision for idtract (spatial component) 139.0890 51.6974 65.6344 129.8213 265.7392 113.4997
Precision for idqtr 15689.3772 13004.2109 2833.3806 12061.7344 50629.7300 7204.0126
Rho for idqtr 0.0333 0.5697 -0.9100 0.0408 0.9369 0.8553
Precision for idqtr1 15689.0194 12897.4501 2811.1477 12112.1103 50679.9925 7238.6445
Precision for idtractqtr 17400.4748 17772.4980 1021.1500 12036.6097 64878.3446 2684.0103

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)